Reason of entropy rise

I'd like to get some more accurate idea of entropy in general: [tex]dS=\int\frac{dQ}{T}[/tex]

Given an adiabatic isolated system. Work is irrerversible done onto this system.

Entropy will rise because of the fact that some of the work is transformed into irreversible losses and therefore [tex]dQ[/tex] increases.

A reversible system will not undergo a rise in entropy because of the fact that no losses will occur, so [tex]dQ=0[/tex] and entropy will remain the same.

Must I also assume that even when the losses are reversible transformable into work again, the transformation is still labelled 'irreversible' . Because losses are inherent factor of a irreversible system (KELVIN) ?